Influence of the crystallographic texture of ITO on the electrodeposition of silver nanoparticles

The electrochemical control over nucleation and growth of metal nanoparticles on foreign substrates is an active field of research, where the surface properties of the substrate have a key role in nucleation dynamics. Polycrystalline indium tin oxide (ITO) films are highly desired substrates for many optoelectronic applications, for which the only parameter that is often specified is the sheet resistance. As a result, growth on ITO is highly irreproducible. Here, we show that ITO substrates with same technical specifications (i.e. sheet resistance, light transmittance and roughness) and supplier may still have different crystalline texture, which we find it has a strong impact on the nucleation and growth of silver nanoparticles during electrodeposition. We find that the preferential presence of lower index surfaces leads to few orders of magnitude lower island density, which is strongly dependent on the nucleation pulse potential. By contrast, the island density on ITO with preferential 〈111〉 orientation is barely affected by the nucleation pulse potential. This work highlights the importance of reporting the surface properties of polycrystalline substrates when presenting nucleation studies and metal nanoparticle electrochemical growth.

S2 Potential scheme of the double pulse technique Figure S5 shows the potential scheme as used in the double pulse technique. First, the experiment starts with initializing for 5 seconds at OCP (of which varies between samples), followed by the nucleation and growth pulse. The lowest and highest nucleation pulse potential used are 0.2 V vs Ag/AgCl and -0.883 V vs Ag/AgCl as indicated by the green dashed and red solid line, respectively. Note that the x-axis for the nucleation pulse was stretched to highlight the pulse shape.  Figure S6 show the first and second cycle of the cyclic voltammogram of batch 1 (red) and batch 2 (green). Due to the incomplete stripping of the deposited silver, the large nucleation overpotential is significantly decreased in the second cycle of the cyclic voltammogram for both batches. This is because the silver is now also able to nucleate on the already existing silver nuclei which were formed during the first cycle. This effect is more pronounced for batch 1 than batch 2.

S3 Cyclic voltammograms
The experimental Nernst equilibrium potential E 0 Ag/Ag + was determined by extracting the halfway potential from the second cycle of the saccharine electrolyte. Since for batch 2 most of the silver was stripped, the onset potential of the second cycle is still significant and hence the cathodic peak is shifted to more negative potentials. Therefore, for batch 2 the halfway potential of the blank electrolyte was used instead (which is very similar to the found value for batch 1). The corresponding free silver ion concentration was found to be 0.26 mM.

S4 SEM data treatment
The obtained SEM images were analysed using a python script which is based on a watershed image recognition method. From these images, the particle density and size distribution were extracted. The SEM images were analysed using the OpenCV package in python (https://opencv.org/). A threshold of the raw SEM image was obtained using the adaptiveThreshold function. The image was then split into a sure foreground, and a sure background image. The difference between these images was used in a watershed method to determine the contour of the edges. The final contours and thus the area of the particles were obtained by using the function connectedComponentsWithStats. One example of an analysed SEM image is shown in figure S7. The contour of the found particles is shown in red. Particles which were lying on the outline of the image were discarded from the analyses.  Figure S8 shows the size distribution of the selected samples shown in the SEM images in figure 3. The size distributions moves to smaller radii as the nucleation pulse overpotential increases. Although it seems that the distribution becomes more narrow, the relative standard deviation (RSD = SD/r mean ) is constant and might even slightly increase (especially for batch 1). For each SEM image such a distribution is obtained. Per sample (applied nucleation pulse overpotential), multiple size distributions were obtained. These distributions were merged such that there is only one size distribution per nucleation pulse overpotential. From the final size distribution per nucleation pulse overpotential, one can obtain the mean island radius r mean . Figure S9 shows the mean island radius as function of the corresponding island density for both batch 1 (red) and batch 2 (green). From this figure it is clear that the mean island radius is determined by the island density, irrespective of the used nucleation pulse overpotential.

S5 Particle size distribution
The mean island radius as function of nucleation pulse overpotential is shown in figure S10. The mean island radius of batch 1 decreases with increasing nucleation pulse overpotential up to a value of 0.8 V, after which it stays constant. A similar trend for batch 2 is observed, although it is not clear whether batch 2 also reaches a constant value due to the lack of data points.

S6 Transferred charge calculation
The total transferred charge can be calculated in two ways. The first and simplest method is by integrating the current to obtain the total amount of transferred charge Q: The second method is by combining the obtained island density with the mean radius of the particles (see figures S9). From these parameters, one can calculate an effective volume by assuming that the islands are spherical.
where ⟨r⟩ is the mean radius of the islands, and N is the total amount of islands which can be obtained by multiplying the island density ρ with the total exposed area A (0.95 cm 2 ). The total amount of deposited volume can than be converted into a expected transferred charge by using the constant of Faraday F, the molar mass M Ag and density ρ Ag of silver. The total expected transferred charge can then be calculated by: (S3) Figure S11a shows the amount of transferred charge (deposited silver) and figure S11b shows the amount of expected transferred charge both as function of the island density, where samples from batch 1/2 are shown as circles/squares. Here, the shade of red/green of each data point indicates the nucleation pulse overpotential that was used for that sample.
In batch 1 samples, which exhibit a large spread in the island density for this nucleation potential range, two growth regimes can be discerned. At low island densities (i.e. below 10 8 cm −2 ), the amount of transferred charge increases with island density. This behaviour agrees well with an uncoupled growth regime, where each silver islands grows independently with an unrestricted supply of Ag + ions. By contrast, once the island density increases beyond 10 8 cm −2 , ion diffusion becomes restricted by neighbouring islands, which leads to the diffusion-coupled growth regime. Given the consistently larger density of silver islands in batch 2 samples, the silver island growth is always in the diffusion-coupled regime in agreement to the behaviour observed in batch 1 samples with similar island density. Fig. S11 a) Total transferred charge, obtained from integrating the current, as function of island density, and b) the total equivalent transferred charge, obtained from the island density and mean radius, as function of island density. The color bar indicates the used nucleation pulse overpotential for batch 1 (red) and batch 2 (green) samples.

S7 Nearest Neighbour distance analyses
In the nearest neighbour distance (nnd) analyses, the distances between each island and its nearest neighbour is compared to the expected values for a spatially random point pattern, to determine if the sample obeys complete spatial randomness (CSR). For a random point pattern, the nnd distribution should be following a Poisson distribution.
The SEM images were treated as described in section S4, from which the centroid of each island was extracted for all individual SEM images. The nnd was calculated by finding the minimum distance between the centroid of a given island and the centroid of all the other island present in that image. In order to get a decent amount of points for the histogram, the nnd of multiple SEM images per sample were combined to a single nnd histogram. The bin size of the histograms is not relevant for the calculation of the Z-score (see eq 6), since only the mean value of the nnd distribution is used. Hence, the number of bins was chosen to be 14 for the histograms shown in figure 5a) to c).
The probability density function (pdf) for a random pattern (Poisson distribution) is derived in the work of Guo et al.,36 and is summarized below: The probability of finding n particles in an area A = πr 2 is given by: where ρ is the island density (assumed to be zero-volume particles).
To derive the pdf for the first order, one needs to consider the probability of finding no particles within an area of radius r from a arbitrary particle. This probability of finding zero particles within a radius r is given by (n=0): Therefore, the probability of finding at least one particle between a radius r and r + dr is then given by: At last the pdf p(r) can be found by differentiating the equation above, and is given by: dP(r) = p(r)dr = 2πρr exp(−ρπr 2 )dr (S7) To to derive the pdf for the second and higher orders, one needs now to consider the probability of finding at least two particles inside a radius r, which is given by: Fig. S12 Z-value obtained from individual second nnd distributions as function of the island density. Samples from batch 1 and 2 are indicated by red circles and green squares, respectively. The black horizontal dashed lines indicates the region for which the distribution of islands exhibit CSR. and hence, dP(r) = p(r)dr = 2πρr exp(−ρπr 2 )dr + 2ρ 2 π 2 r 3 exp(−ρπr 2 )dr − 2πρr exp(−ρπr 2 )dr = 2ρ 2 π 2 r 3 exp(−ρπr 2 )dr (S9) Once the pdf is known, the mean nnd and variance can be obtained by: The Z-value is defined in the main manuscript. The Z-values as function of island density for the first nnd are shown in the main manuscript in figure 6. The Z-values as function of the island density for the second nnd is shown in figure S12. The trend of both graphs are similar, indicating that sample with a higher particle density do in general not obey CSR.